In many technical fields there is a need for measuring the topography and tomography of objects. There are many optical methods for accomplishing the task such as the structured-light scanning method, confocal microscopy, phase shifting interferometry (PSI), optical coherence tomography (OCT) or holography.
In PSI, light is split by an interferometer to two beams, the object beam and the reference beam, and interference is generated between the object beam that is reflected from an inspected object, and the reference beam that is reflected from a reference mirror. A movement of the reference mirror induces a phase shift between the two beams and the resulting changing interference patterns are acquired by a 2D camera. From at least three different interference patterns, taken at different positions of the reference mirror, the object's surface is obtained with high accuracy. However, this method requires a temporal coherent light source and suffers from the 2π ambiguity problem. Hence, the accuracy is very high, in the order of sub wavelengths, but the dynamic-range is small.
In low coherence interferometry such as in OCT or While Light Interferometry (WLI), the light is split by a beam splitter in an interferometer to two beams, the object beam that is reflected from an inspected object and the reference beam that is reflected from a reference mirror. The returning beams are relayed by the beam splitter to a 2D imager, and form an interference pattern of the object's surface topography that is spatially sampled by the 2D imager pixels. However, the interference patterns are obtained only if the two beams have traveled optical paths with an Optical Path Difference (OPD) that is less than the coherence length of the light source.
The coherence length of a broadband light source is the width of the envelope of the coherence function of the light source which is the autocorrelation function of the light field. According to the Wiener-Khintchine theorem, the autocorrelation function of the light field is given by the Fourier transformation of the spectral density of the light source.
As an example, FIG. 1a shows the spectral density function of a Gaussian spectrum light source where the normalized spectral density function of the light source is:
      S    ⁡          (      v      )        =            1                        π                ⁢        Δ        ⁢                                  ⁢        v              ⁢          exp      ⁡              [                  -                                    (                                                (                                      v                    -                                          v                      0                                                        )                                                  Δ                  ⁢                                                                          ⁢                  v                                            )                        2                          ]            
2Δν is the effective 1/e-bandwidth and ν0 is the mean frequency.
According to the Wiener-Khintchine theorem, the autocorrelation function of the light field is given by:k(τ)=∫−∞∞S(ν)exp(−i2πντ)dν=exp(−π2τ2ν2)exp(−i2πν0τ)
The autocorrelation function is shown in FIG. 1b. This function represents the intensity of the interference patterns of two beams reflected from both Michelson interferometer's arms as a function of τ—the time delay between the two beams which depends on the OPD between them by:
  τ  =      OPD    c  where c is the speed of light.
Fringes with visible contrast are obtained only when the OPD lies within the coherence length of the light source. When the OPD is larger than the coherence length, the fringes are invisible and the illumination is the average illumination. The contrast of the fringes is determined by the envelope of the coherent function and the period of the fringes (or modulations) inside the envelope is λ0/2, where λ0 is the mean wavelength of the light source. Accordingly, a broadband light source may be considered as a monochromatic light with the wavelength λ0 and may be used for any kind of long coherence interferometry process as long as the OPD between the two interfering beams is shorter than the coherence length of the light source.
In short coherence interferometry, measurement of an object surface is done by changing the OPD between the measurement beam and the reference beam using a positioning stage when the measurement beam is reflected from the object and the reference beam is reflected from a reference surface. In this case as the OPD is changed constantly as a function of time and an interferogram is generated at each pixel. As mentioned above, the range of OPDs where the fringes of the interference are visible is the coherence length of the light source which depends on its spectral width. The maximum modulation of the interference signal of a pixel occurs when the OPD between the measurement beam and the reference beam is zero. Therefore, the optical distance of a point on the surface of the measured object imaged at this pixel relative to the reference surface corresponds to the OPD between this point and the reference surface, and it can be determined by noting when the modulation of the interference fringes is greatest. A matrix with the height values of the object surface can be derived by determining the z-values of the positioning stage where the modulation is greatest for every pixel. The lateral positions of the height values depend on the corresponding object point that is imaged by the pixel matrix. These lateral coordinates, together with the corresponding vertical coordinates, describe the surface topography of the object.
Although the dynamic-range of the WLI measurements is large (hundreds of microns), the accuracy is limited to the accuracy of defining the position where the modulation of the interference fringes is greatest, and is in the order of microns.
U.S. Pat. No. 5,953,124 discloses methods where both a phase shifting interferometry (PSI) analysis and a scanning white light interferometry (SWLI) analysis are applied to a single 3D interferogram. This allows the precision of PSI to be achieved without being limited by the 2π phase ambiguity constraint. The envelopes of the coherent functions of two reflected beams from two pixels of the object should overlap in order to compare the two calculated phases of the reflected light from these two pixels. In tomography there are several wave packets or envelopes that are reflected from different layers at each pixel, each from each object's layer. The accuracy of the tomography measurements can be increased by comparing between the calculated phases of all envelopes of each same pixel. Comparison between the respective phases of all envelopes of different pixels also increases the accuracy not only of the tomography measurement but also the topography measurement of the measured object.